Exporting to Unity - Origin problems
I had the exact same problem, but for me the origin in Unity was always the center of the part. 

It turns out that there's a setting in Unity that determines how the axes are shown for the part. I spent probably three hours trying to troubleshoot what was wrong in the process. 



There was no problem with how I had exported the part, just with how Unity was displaying the part handle. When I clicked "Center" it changed to "Pivot" and then the axes were shown from the same location as I had set the part origin in Blender.